Analysis of genetic code properties by mathematical simulation

We consider random changes in the standard genetic code, under which its structure is preserved, as well as small variations of the genetic code in which the structure is preserved or changed. It justifies the assumption that the standard genetic code in the best way provides the possibility of gene overlap. The structure and content of the standard genetic code is determined by the condition of the maximum total number of allowable substitutions that open the closed reading frames and the minimal closed reading frames for which there is no such replacement. The estimated probability of a random selection of a standard genetic code from the point of view of this criterion, depending on the model of a numerical experiment, is of the order of $10^{-3}$ to $10^{-6}$.